1. Field of the Invention
The invention relates to the field of radars with digital pulse compression and, more particularly, to the field of short-range radars.
However, its scope can be broadened, and it can be used in the field of analog pulse compression radars and telecommunications receivers receiving signals that have a low level in relation to the noise.
2. Description of the Prior Art
It is known that short-range radars send out a series of pulses with a duration N.tau.. In this expression, N designates an integer and .tau. designates an elementary instant of the pulse. Each of the elementary instants of the pulse is modulated by a variation of a parameter of the transmission. This parameter may be, for example, the phase or the frequency. Thus, for duration N.tau. may or may not be assigned a phase shift .pi.. By convention, the phase 0 (coefficient 1) shall be taken for the binary code 1 and the phase .pi. (coefficient -1) shall be taken for the binary number 0.
The signals received, which include noise and the return echo from a target if any, are compared with the transmitted wave by being passed through a correlator.
The correlation of two functions gives the measure of the resemblance existing between them: it is essentially a method of comparison.
In digital terms, the signals are represented by sequences of numbers which are successive samples of a continuous waveform.
The function of correlation of f(k) and g(k), the two digital sequences obtained by the sampling of two continuous functions f(t) and g(t), is expressed mathematically by the relationship: ##EQU1##
with i=index of the sample
and k=index of the shift
When f and g are different functions, the term used is "intercorrelation".
When f and g are identical functions, the term used is "self-correlation".
The function of self-correlation S(k) of a code of N instants represented by the sequence C.sub.i (i ranging from 0 to N-1) is the measure of the resemblance existing between the code and itself, shifted by a number k of instants. ##EQU2##
The result of the self-correlation of a code with a duration of N instants is a sequence of numbers that represents the amplitude of the signal as a function of the successive shifts that are applied to it, it being possible for these shifts to be graduated in time or in distance since, in radar, ##EQU3##
The self-correlation function is symmetrical: EQU S(k)=S(-k)
It gives a main peak and side lobes.
______________________________________ Thus, between the code with five instants 11101 and this same code shifted by 0 11101 ______________________________________
There are five resemblances whence S(0)=5.
______________________________________ To compute S(1) 11101 Code shifted by 1 11101 ______________________________________
There are two resemblances and two differences, whence S(1)=0.
______________________________________ To compute S(2) 11101 Code shifted by 2 11101 ______________________________________
There are two resemblances and one difference, whence S(2)=1.
In the same way, we find S(3)=0, S(4)=1.
The number of resemblances of a code with N instants in relation to itself shifted in time is the maximum for a zero shift and is equal to N.
S(0)=N
S(0) is the main peak, with a width equal to a shift. It gives the distance of the target.
For the other shifts, with k ranging from 1 to N-1, the self-correlation gives a smaller result, which may be zero. This result depends solely on the code chosen. These results are the side lobes: they are on either side of the main peak and are symmetrical, S(k) being equal to S(-k).
If a side lobe of a code with N instants has the value m, its attenuation in decibels in relation to the major lobe is equal to: EQU lobe i=20 log m/N.
If we again take up the example of the code with five instants 11101, the representation in time of its self-correlation function is shown in FIG. 1, for k varying from -5 to +5.
This function reveals a major lobe for k=0 and 4 side lobes with a value 1.
The relative level of the side lobes is: 20 log(1/5)=14 dB.
An example with a two-phased code has just been seen.
Two-phased codes are only a particular case of polyphased codes where the coefficients are complex numbers (n-th roots of unity).
two-phased codes: 1 -1
quadriphased codes: 1 j-1 -j
There is another way of defining the correlation, in using the plane of the complex numbers.
The phase code with a length of N instants used at transmission may be represented in the complex plane in the form of an N-1 degree polynomial C(z), conventionally defined on the variable z this variable represents a temporal shift of one where the rank of the sample and the phases of the code define the coefficients (+1 or -1 in the case of a two-phase code).
The two-phase code with five instants 11101 may be depicted in the form of a 4th degree polynomial: EQU C(z)=1+z.sup.-1 +z.sup.-2 -z.sup.-3 +z.sup.-4
The reference code CR(z) adapted to the code C(z) corresponds to the conjugate complex code of C(z), temporally inverted. Indeed, when a code C(z) is self-correlated by its replica CR(z) in a digital correlator, this replica should be the conjugate of the initial code inverted in time:
for EQU C(z)=1+z.sup.-1 +z.sup.-2 -z.sup.-3 +z.sup.-4
The code 11101 should first of all receive 1 (stage 1 of the digital correlator), then -1 (stage 2) and finally 3 times 1 (stages 3, 4, 5):
whence: EQU CR(z)=1-z.sup.-1 +z.sup.-2 +z.sup.-3 +z.sup.-4
This operation, which can be explained physically, is equivalent to the transformation of z into 1:z and to the addition of a delay. In the case of the polyphased codes, it is necessary in addition to take the conjugate coefficient: EQU CR(z)=C*(1/z).multidot.z.sup.-(n-1)
that is, a code: 11j-j-1
It can be written thus: EQU C(z)=1+z.sup.-1 +jz.sup.-2 -jz.sup.-3 -z.sup.-4
The matched code is: EQU CR(z)=-1+jz.sup.-1 -jz.sup.-2 +z.sup.-3 +z.sup.-4
In the correlator, the coefficients should be arranged thus:
______________________________________ stage 1 2 3 4 5 coefficient -1 j -j 1 1 ______________________________________
The correlation function S(z) is expressed thus: EQU S(z)=C(z).multidot.CR(z)=C(z).C*(1/z).z.sup.-(n-1)
In the example of the code 11101: ##EQU4##
The result obtained in the example where the same code was simply two-phased is found again: 101050101 with a main peak at 5 and the side lobes at 1.
The correlation operations are done for all the distances of the range of the radar, i.e. every C.tau./2. This means that the correlation operation should be carried out every .tau.. The corresponding polynomials are therefore assigned a factor z.sup.-m representing the different delays.
Radar designers have been led to use pulse compression to improve the resolution in distance.
Starting from a standard radar sending out pulses with a duration T shown in FIG. 2a, the response obtained at output of a matched filter is shown in FIG. 2b.
In these figures, it is seen that a square-wave signal with a duration T corresponds to a saw-toothed self-correlation function leading to an uncertainty over the distance of the target.
By building a pulse compression radar that sends out pulses with a width of T=N.tau., it is sought to achieve the ideal response.
The transmitted signal and the corresponding self-correlation function are shown in FIGS. 3a and 3b.
The transmitted signal comprises a code with five instants 11101 (the code of the example), the self-correlation function being represented by a peak with a width .tau.. The uncertainty over the distance has been divided by N.
In fact, as shown further above, this ideal response is approached, but for the side lobes.
For each distance, after a processing that depends on the type of radar, the result of the detection is compared with a threshold and all that is above this threshold prompts a detection. It may therefore happen that, under certain conditions (very high echo), the side lobe leads to a detection. This unwanted detection is really prompted by the echo, but at a false distance.
The display of the targets is activated by the detection: the problem of detection therefore relates to the display. The measurements and the computations made in the processing operation lead to the localization of the targets, in terms of both distance and bearing and, in the Doppler radars, they make it possible to ascertain the speed of the detected targets with precision. These information elements can be displayed on a screen, either on a cathode-ray tube or, as is becoming increasingly common, on a digital screen.
The pips, which represent the detected targets, generally represent the width of the transmission pulse in a standard radar and the width of the elementary instant in a pulse compression radar.
Thus, in the case of pulse compression (CI), the side lobes will also prompt pips on the screen, from a certain degree of signal power reflected by the target. This phenomenon will appear as soon as the signal-to-noise ratio of an echo is greater than the rejection of the side lobes.
The side lobes extend over a distance equal to 2N times the width of the elementary instant, the main lobe being located in the middle. Their number will therefore increase concomitantly with an increase in the compression rate.
It has been seen here above that the self-correlation inevitably produces side lobes. Their level depends on the codes employed, whence the importance of the choice of the codes.
For a code with N instants, the major lobe always has the value N.
It has been sought to reduce the value of the side lobes to the minimum. The minimum value that can be obtained is 1. The codes that fulfill the condition of having a maximum number of side lobes equal to 1 are the so-called Barker codes.
The study of these codes has shown that they exist only up to a maximum length of 13 and that, for this value, the level of the side lobes will therefore be: 20 Log 13=22 dB.
It may also be sought to increase the value of the main peak. To achieve this, it is enough to increase N.
The pseudo-random sequences, or maximum length sequences, are especially promising because they have a structure similar to that of the random sequences and have valuable self-correlation functions. A looped shift register generates a pseudo-random sequence in a simple and practical way. After the stages of a shift register have been initialized at 1, an addition modulo 2 is made of the outputs, and the result of this addition constitutes the input of the register. The outputs of the shift register constitute generators of sequences of 0 and 1 which are repeated. These sequences have a length that depends on the loops. When the summed up stages are suitably chosen, a sequence is obtained having a maximum length, for an N-stage register, of: L=2.sup.N -1.
The results of the self-correlation function of these codes give a main peak to side lobe ratio of the order of .sqroot.N.
In practice it is possible, with such codes, to reduce the side lobes to 24 dB below the main peak.
It is also possible to place a code with a length greater than the transmitted reference code in the place of the matched code. This is the mismatched code method.
This method leads to losses that have to be computed in each case. Very satisfactory results can be obtained with losses of the order of 0.2 to 1 dB.
The methods just explained, which are used to reduce the side lobes, all have characteristic qualities and defects:
the Barker codes (with a length N) leave secondary lobes with relatively high levels spread over 2N instants; PA1 the mismatched codes leave the secondary lobes at a low level but spread over far greater distances. PA1 said processing comprising notably an operation of filtering that is matched with the transmitted signal and an operation of detection by the comparison of the post-filtering level of the signal with a so-called detection threshold; PA1 wherein the signal received is subjected to two processing operations A and B, the processing operation A comprising a self-correlation and the processing operation B comprising an intercorrelation with a mismatched code having a length at least equal to 3N, the function of intercorrelation of this mismatched code with the transmission code giving a major central lobe and at least N side lobes that are zero on either side of this major lobe; PA1 and wherein it is decided that there is a detection relating to one of the instants of the correlation or of the intercorrelation only if the levels of the functions of self-correlation and intercorrelation of this very same instant are higher than the detection threshold.
The attenuations obtained are generally sufficient for long-range radars. By contrast, short-range radars generally have very substantial dynamic ranges of signals.
The unwanted detections due to the secondary lobes, which are appreciable especially with short-range radars, have many drawbacks, particularly when it is sought to provide the radar with special functions such as, for example, the acquisition and automatic tracking of moving targets. When a target is determined, its position is determined and the radar remains aimed at it. It follows its movements both in distance and in relative bearing, and remains "locked on" as long as the operator wishes it.
This method can work accurately only if the target is precisely localized. The presence of side lobes may lead to difficulties in tracking a moving target. Similarly, when a protected site has to be monitored by means of a radar, there may be zones (for example roads, etc.) where the presence of moving targets is normal. In this case, the detections should not prompt alarms, and these zones need to be inhibited. The monitoring of perimeters is a particular example of the management of zones: the radar monitors a portion of ground with a determined width (for example the rim of a protected site) and should raise an alarm only for targets moving in this zone. Targets located within inhibited zones may prompt detections in adjacent zones through their side lobes which are located within the active monitoring zone and thus prompt unwanted detections.